Method, computer program product, and system for risk management

Abstract

Described are a method, computer program product, and system for risk management using readily available, gridded hazard data to estimate and obtain a risk analysis parameter (e.g., expected repair cost) for use in risk management, such as in seismic risk management. The method includes calculating economic risk for buildings in terms of an expected annualized loss (EAL). EAL is the product of a scenario loss estimate called probable frequent loss (PFL) and an economic hazard coefficient (H). H can be created using readily available gridded hazard data produced by the U.S. Geological Survey. The method also includes a technique for calculating shaking intensity, s EBE , which is needed for determining PFL. Incorporated into a system, the system can be utilized by engineering consultants (or others interested in risk management) via the Internet, or on any other computer readable medium.

1. A computer-implemented method for obtaining a seismic risk analysis, the method comprising an act of:
 causing a computer processor to execute instructions specifically encoded on a memory, such that upon execution, the computer processor performs operations of: 
 a. receiving, by the computer processor, as input a planning period t EBE , where the planning period is the period an investor uses in a financial analysis of an economic-basis earthquake for a particular facility; 
 b. calculating, by the computer processor, a risk analysis parameter based upon the planning period t EBE ; and 
 c. calculating, by the computer processor, an expected annualized loss (EAL) according to the following:
   EAL= H ×PFL,
 
 
  wherein PFL represents a probable frequent loss, an average loss conditioned on a seismic intensity associated with the economic-basis earthquake, and H represents an economic hazard coefficient; and 
 d. determining, by the computer processor, the EAL in order to provide an expected annualized value of repair cost to the particular facility in a particular location; 
 wherein in the act of calculating a risk analysis parameter, the risk analysis parameter is hazard coefficient H, and the act of calculating hazard coefficient H further comprising acts of: 
 a. calculating G EBE , where G EBE  is an average exceedance frequency of s EBE , and where s EBE  is the seismic intensity associated with an economic-basis earthquake; 
 b. identifying grid points closest to ô for location ô=({circumflex over (φ)}, {circumflex over (λ)}), where {circumflex over (φ)} denotes a latitude designation and {circumflex over (λ)} denotes a longitude designation, the grid points closest to ô being referred to as the bounding grid points o j ; 
 c. considering the period of interest {circumflex over (T)}, determining a period of at least one hazard curve, referred to as a bounding period T i ; 
 d. letting s r,k  denote the k th  value (k=1, 2, . . . n s ) of s r  in the hazard curve G(s r |o j ,c=c r ,T=T i ,ζ=ζ r ) and adjusting s r,k  for each bounding grid point o j  and bounding period T i  to account for site classification ĉ and for damping ratio {circumflex over (ζ)}, where s is seismic intensity and where adjusting s r,k  is done by multiplying s r,k  by a site-classification coefficient F c  and a damping coefficient F ζ , where by denoting by s k  the k th  value of s at the same location and period after adjusting for site classification and damping ratio,
     G ( s   k   |o   j   ,c=ĉ,T=T   i ,ζ={circumflex over (ζ)})= G ( F   c   F   ζ   s   r,k   |o   j   ,c=c   r   ,T=T   i ,ζ=ζ r ): k= 1, 2 , . . . n   s ;
 
 
 e. letting G i,j,NZ  denote the damping- and site-class-adjusted average exceedance frequency of s NZ  given period T i  and location o j , and for each T i  and o j , interpolating each curve from “Act d” to determine G i,j,NZ ; 
 f. letting G j,NZ  denote the damping- and site-class-adjusted value of G NZ  at the period of interest {circumflex over (T)} and location o j , and for each j, calculating G j,NZ ; 
 g. letting G NZ  denote the damping- and site-class-adjusted value of G NZ  at the period of interest {circumflex over (T)} and location of interest ô, and calculating G NZ ; 
 h. calculating risk analysis parameter H (i.e., hazard coefficient) according to the following: 
 
       
         
           
             
               
                 H 
                 ≡ 
                 
                   
                     G 
                     NZ 
                   
                   
                     ln 
                     ⁡ 
                     
                       ( 
                       
                         
                           G 
                           NZ 
                         
                         / 
                         
                           G 
                           EBE 
                         
                       
                       ) 
                     
                   
                 
               
               , 
             
           
         
       
       whereby through H, a user may calculate an expected annualized loss (EAL) according to the following:
   EAL= H ×PFL,
 
 
       wherein PFL represents a probable frequent loss, mean loss conditioned on an occurrence of s EBE . 
     
     
       2. A method for obtaining a risk analysis parameter as set forth in  claim 1 , wherein the act of calculating G EBE , G EBE  is calculated based on t EBE  and p EBE  assuming Poisson earthquake arrivals according to the following:
     G   EBE =−ln(1− p   EBE )/ t   EBE ,
 
 where G EBE  is a mean annual exceedance frequency of s EBE , where s EBE  is the seismic intensity associated with an economic-basis earthquake, and where p EBE  is the probability that earthquake shaking of intensity s EBE  or greater will occur during planning period t EBE . 
 
     
     
       3. A method for obtaining a risk analysis parameter as set forth in  claim 1 , wherein the act of identifying grid points closest ô for location ô=({circumflex over (φ)}, {circumflex over (λ)}), further comprises acts of identifying four grid points closest to ô for location ô=({circumflex over (φ)}, {circumflex over (λ)}), where {circumflex over (φ)} denotes a latitude designation and {circumflex over (λ)} denotes a longitude designation, the four grid points closest to ô being referred to as the bounding grid points o 1 =(φ 1 , λ 1 ), o 2 =(φ 1 +Δφ, λ 1 ), o 3 =(φ 1 , λ 1 +Δλ) and o 4 =(φ 1 +Δφ,λ 1 +Δλ)}, where o 1 , o 2 , o 3 , o 4 ε{(φ r , λ r )} such that φ min ≦φ 1 <{circumflex over (φ)}≦φ 1 +Δφ≦φ max  and λ min ≦λ 1 <{circumflex over (λ)}≦λ 1 +Δλ≦λ max , and calculating x and y according to the following:
     x =({circumflex over (φ)}−φ 1 )/(Δφ) and  y =({circumflex over (λ)}−λ 1 )/(Δλ).
 
 
     
     
       4. A method for obtaining a risk analysis parameter as set forth in  claim 1 , wherein the act of determining a period of at least one hazard curve, further comprises an act of determining periods of two hazard curves, referred to as bounding periods, T 1 , T 2 ε{T r }, such that T 1 <{circumflex over (T)}≦T 2 , or T 1 ={circumflex over (T)} if {circumflex over (T)} is in {T r } and is equal to its minimum value, and T 1  is the maximum value of {T r } satisfying these conditions and T 2  is the minimum value of {T r } satisfying these conditions. 
     
     
       5. A system for obtaining a seismic risk analysis parameter, the system comprising:
 a computer having a memory and a processor, the memory encoded with instructions for causing the computer to perform operations of: 
 a. receiving as input a planning period t EBE , where the planning period is the period an investor uses in a financial analysis of an economic-basis earthquake for a particular facility; 
 b. calculating a risk analysis parameter based upon the planning period t EBE ; 
 c. calculating an expected annualized loss (EAL) according to the following:
   EAL= H ×PFL,
 
 
 
       wherein PFL represents a probable frequent loss, an average loss conditioned on a seismic intensity associated with the economic-basis earthquake, and H represents an economic hazard coefficient; and
 d. determining the EAL in order to provide an expected annualized value of repair cost to a particular facility in the particular location; 
 wherein in the operation of calculating a risk analysis parameter, the risk analysis parameter is hazard coefficient H, and the operation of calculating hazard coefficient H further comprising operations of: 
 a. calculating G EBE , where G EBE  is an average exceedance frequency of s EBE , and where s EBE  is the seismic intensity associated with an economic-basis earthquake; 
 b. identifying grid points closest to ô for location ô=({circumflex over (φ)}, {circumflex over (λ)}), where {circumflex over (φ)} denotes a latitude designation and {circumflex over (λ)} denotes a longitude designation, the grid points closest to ô being referred to as the bounding grid points o j ; 
 c. considering the period of interest {circumflex over (T)}, determining a period of at least one hazard curve, referred to as a bounding period T i ; 
 d. letting s r,k  denote the k th  value (k=1, 2, . . . n s ) of s r  in the hazard curve G(s r |o j ,c=c r ,T=T i ,ζ=ζ r ) and adjusting s r,k  for each bounding grid point o j  and bounding period T i  to account for site classification ĉ and for damping ratio ζ, where s is seismic intensity and where adjusting s r,k  is done by multiplying s r,k  by a site-classification coefficient F c  and a damping coefficient F ζ , where by denoting by s k  the k th  value of s at the same location and period after adjusting for site classification and damping ratio,
     G ( s   k   |o   j   ,c=ĉ,T=T   i ,ζ={circumflex over (ζ)})= G ( F   c   F   ζ   s   r,k   |o   j   ,c=c   r   ,T=T   i ,ζ=ζ r ): k= 1, 2 , . . . n   s ;
 
 
 e. letting G i,j,NZ  denote the damping- and site-class-adjusted average exceedance frequency of s NZ  given period T i  and location o j , and for each T i  and o j , interpolating each curve from “Act d” to determine G i,j,NZ ; 
 f. letting G j,NZ  denote the damping- and site-class-adjusted value of G NZ  at the period of interest {circumflex over (T)} and location o j , and for each j, calculating G j, NZ ; 
 g. letting G NZ  denote the damping- and site-class-adjusted value of G NZ  at the period of interest {circumflex over (T)} and location of interest ô, and calculating G NZ ; 
 h. calculating risk analysis parameter H (i.e., hazard coefficient) according to the following: 
 
       
         
           
             
               
                 H 
                 ≡ 
                 
                   
                     G 
                     NZ 
                   
                   
                     ln 
                     ⁡ 
                     
                       ( 
                       
                         
                           G 
                           NZ 
                         
                         / 
                         
                           G 
                           EBE 
                         
                       
                       ) 
                     
                   
                 
               
               , 
             
           
         
       
       whereby through H, a user may calculate an expected annualized loss (EAL) according to the following:
   EAL= H ×PFL,
 
 
       wherein PFL represents a probable frequent loss, mean loss conditioned on an occurrence of s EBE . 
     
     
       6. A system for obtaining a risk analysis parameter as set forth in  claim 5 , wherein the operation of calculating G EBE , G EBE  is calculated based on t EBE  and p EBE  assuming Poisson earthquake arrivals according to the following:
     G   EBE =−ln(1− p   EBE )/ t   EBE ,
 
 where G EBE  is a mean annual exceedance frequency of s EBE , where s EBE  is the seismic intensity associated with an economic-basis earthquake, and where p EBE  is the probability that earthquake shaking of intensity s EBE  or greater will occur during planning period t EBE . 
 
     
     
       7. A system for obtaining a risk analysis parameter as set forth in  claim 5 , wherein the operation of identifying grid points closest ô for location ô=({circumflex over (φ)}, {circumflex over (λ)}), further comprises operations of identifying four grid points closest to ô for location ô=({circumflex over (φ)}, {circumflex over (λ)}), where {circumflex over (φ)} denotes a latitude designation and {circumflex over (λ)} denotes a longitude designation, the four grid points closest to ô being referred to as the bounding grid points o 1 =(φ 1 , λ 1 ), o 2 =(φ 1 +Δφ, λ 1 ), o 3 =(φ 1 , λ 1 +Δλ) and o 4 =(φ 1 +Δφ,λ 1 +Δλ)}, where o 1 , o 2 , o 3 , o 4 ε{(φ r , λ r )} such that φ min ≦φ 1 <{circumflex over (φ)}≦φ 1 +Δφ≦φ max  and λ min ≦λ 1 <{circumflex over (λ)}≦λ 1 +Δλ≦λ max , and calculating x and y according to the following:
     x =({circumflex over (φ)}−φ 1 )(Δφ) and  y =({circumflex over (λ)}−λ 1 )/(Δλ).
 
 
     
     
       8. A system for obtaining a risk analysis parameter as set forth in  claim 5 , wherein the operation of determining a period of at least one hazard curve, further comprises an operation of determining periods of two hazard curves, referred to as bounding periods, T 1 , T 2 ε{T r }, such that T 1 <{circumflex over (T)}≦T 2 , or T 1 ={circumflex over (T)} if {circumflex over (T)} is in {T r } and is equal to its minimum value, and T 1  is the maximum value of {T r } satisfying these conditions and T 2  is the minimum value of {T r } satisfying these conditions. 
     
     
       9. A system for obtaining a risk analysis parameter as set forth in  claim 5 , wherein the operations of letting s r,k  denote the k th  value and adjusting s r,k , s r,k  is adjusted for each bounding grid point o j  (j=1, 2, 3, 4) and bounding period T i  (i=1,2) to account for site classification ĉ and for damping ratio {circumflex over (ζ)}, where s is seismic intensity and where adjusting s r,k  is done by multiplying s r,k  by a site-classification coefficient F c  and a damping coefficient F ζ , where by denoting by s k  the k th  value of s at the same location and period after adjusting for site classification and damping ratio,
     G ( s   k   |o   j   ,c=ĉ,T=T   i ,ζ={circumflex over (ζ)})= G ( F   c   F   ζ   s   r,k   |o   j   ,c=c   r   ,T=T   i ,ζ=ζ r ): k= 1, 2 , . . . n   s .
 
 
     
     
       10. A computer program product executable by a computer processor for obtaining a seismic risk analysis parameter, the computer program product comprising:
 computer-readable instructions stored on a non-transitory computer readable medium for causing a computer, when executed by the computer processor, to perform operations of: 
 a. receiving as input planning period t EBE , where the planning period is the period an investor uses in a financial analysis of an economic-basis earthquake for a particular facility; 
 b. calculating a risk analysis parameter based upon the planning period t EBE , 
 c. calculating an expected annualized loss (EAL) according to the following:
   EAL= H ×PFL,
 
 
 
       wherein PFL represents a probable frequent loss, an average loss conditioned on a seismic intensity associated with the economic-basis earthquake, and H represents an economic hazard coefficient; and
 d. determining the EAL in order to provide an expected annualized value of repair cost to a particular facility in the particular location; 
 wherein in the operation of calculating a risk analysis parameter, the risk analysis parameter is hazard coefficient H, and the operation of calculating hazard coefficient H further comprising operations of: 
 a. calculating G EBE , where G EBE  is an average exceedance frequency of s EBE , and where s EBE  is the seismic intensity associated with an economic-basis earthquake; 
 b. identifying grid points closest to ô for location ô=({circumflex over (φ)}, {circumflex over (λ)}), where {circumflex over (φ)} denotes a latitude designation and {circumflex over (λ)} denotes a longitude designation, the grid points closest to ô being referred to as the bounding grid points o j ; 
 c. considering the period of interest {circumflex over (T)}, determining a period of at least one hazard curve, referred to as a bounding period T i ; 
 d. letting s r,k  denote the k th  value (k=1, 2, . . . n s ) of s r  in the hazard curve G(s r |o j ,c=c r ,T=T i ,= r ) and adjusting s r,k  for each bounding grid point o j  and bounding period T i  to account for site classification ĉ and for damping ratio {circumflex over (ζ)}, where s is seismic intensity and where adjusting s r,k  is done by multiplying s r,k  by a site-classification coefficient F c  and a damping coefficient F, where by denoting by s k  the k th  value of s at the same location and period after adjusting for site classification and damping ratio,
     G ( s   k   |o   j   ,c=ĉ,T=T   i ={circumflex over (ζ)})= G ( F   c   F s   r,k   |o   j   ,c=c   r   ,T=T   i ,= r ): k= 1, 2 , . . . n   s ;
 
 
 e. letting G i,j,NZ  denote the damping- and site-class-adjusted average exceedance frequency of s NZ  given period T i  and location o j , and for each T i  and o j , interpolating each curve from “Act d” to determine G i,j,NZ ; 
 f. letting G j,NZ  denote the damping- and site-class-adjusted value of G NZ  at the period of interest {circumflex over (T)} and location o j , and for each j, calculating G j,NZ ; 
 g. letting G NZ  denote the damping- and site-class-adjusted value of G NZ  at the period of interest {circumflex over (T)} and location of interest ô, and calculating G NZ ; 
 h. calculating risk analysis parameter H (i.e., hazard coefficient) according to the following: 
 
       
         
           
             
               
                 H 
                 ≡ 
                 
                   
                     G 
                     NZ 
                   
                   
                     ln 
                     ⁡ 
                     
                       ( 
                       
                         
                           G 
                           NZ 
                         
                         / 
                         
                           G 
                           EBE 
                         
                       
                       ) 
                     
                   
                 
               
               , 
             
           
         
       
       whereby through H, a user may calculate an expected annualized loss (EAL) according to the following:
   EAL= H ×PFL,
 
 
       wherein PFL represents a probable frequent loss, mean loss conditioned on an occurrence of s EBE . 
     
     
       11. A computer program product for obtaining a risk analysis parameter as set forth in  claim 10 , wherein the operation of calculating  GEBE, GEBE  is calculated based on  tEBE  and  pEBE  assuming Poisson earthquake arrivals according to the following:
     G   EBE =−ln(1− p   EBE )/ t   EBE ,
 
 where G EBE  is a mean annual exceedance frequency of s EBE , where s EBE  is the seismic intensity associated with an economic-basis earthquake, and where p EBE  is the probability that earthquake shaking of intensity s EBE  or greater will occur during planning period t EBE . 
 
     
     
       12. A computer program product for obtaining a risk analysis parameter as set forth in  claim 10 , wherein the operation of identifying grid points closest ô for location ô=({circumflex over (φ)}, {circumflex over (λ)}), further comprises operations of identifying four grid points closest to ô for location ô=({circumflex over (φ)}, {circumflex over (λ)}), where {circumflex over (φ)} denotes a latitude designation and {circumflex over (λ)} denotes a longitude designation, the four grid points closest to ô being referred to as the bounding grid points o 1 =(φ 1 , λ 1 ), o 2 =(φ 1 +Δφ, λ 1 ), o 3 =(φ 1 , λ 1 +Δλ) and o 4 =(φ 1 +Δφ,λ 1 +Δλ)}, where o 1 , o 2 , o 3 , o 4 ε{(φ r , λ r )} such that φ min ≦φ 1 <{circumflex over (φ)}≦φ 1 +Δφ max  and λ min ≦λ 1 <{circumflex over (λ)}≦λ 1 +Δλ≦λ max , and calculating x and y according to the following:
     x =({circumflex over (φ)}−φ 1 )/(Δφ) and  y =({circumflex over (λ)}−λ 1 )/(Δλ).
 
 
     
     
       13. A computer program product for obtaining a risk analysis parameter as set forth in  claim 10 , wherein the operation of determining a period of at least one hazard curve, further comprises an operation of determining periods of two hazard curves, referred to as bounding periods, T 1 , T 2 ε{T r }, such that T 1 <{circumflex over (T)}≦T 2 , or T 1 ={circumflex over (T)} if {circumflex over (T)} is in {T r } and is equal to its minimum value, and T 1  is the maximum value of {T r } satisfying these conditions and T 2  is the minimum value of {T r } satisfying these conditions.